You will hopefully have plenty to work on once the lessons start. Your teacher should give you enough to work on throughout the week, and then some.
Try to stay on task, it will lead to better results. Too many students try to do their own thing and don't see the results they expected, so they quit the instrument.

As Sonny said, play along to your favorite bands (unless is Meshuggah, then you are SOL), its a great way to have fun while playing, and can actually help with timing when you are first starting out.

Enjoy, good luck with the parents and hopefully you develop the lifetime love of the drums that most of us acquired.